In the same half of the draw, Rose plays Hunter Mahan, while at the bottom of the draw Padraig Harrington meets Anders Hansen and Montgomerie faces six-time winner Ernie Els.
Out went nine of the players who started Saturday's 1-1 draw at Anfield, and in came a host of fresh faces including the teenage attacker Callum McManaman, who acquitted himself well until forced off by injury just before the break.